// ----------------------------------------------------------------------------
//  This confidential and proprietary software may be used only as authorised
//  by a licensing agreement from Arm Limited.
//      (C) COPYRIGHT 2011-2020 Arm Limited, ALL RIGHTS RESERVED
//  The entire notice above must be reproduced on all authorised copies and
//  copies may only be made to the extent permitted by a licensing agreement
//  from Arm Limited.
// ----------------------------------------------------------------------------

/**
 * @brief Functions to pick best ASTC endpoint for a block.
 */

#include "astc_codec_internals.h"

#ifdef DEBUG_PRINT_DIAGNOSTICS
	#include <stdio.h>
#endif

/*
   functions to determine, for a given partitioning, which color endpoint formats are the best to use.
 */

// for a given partition, compute for every (integer-component-count, quantization-level)
// the color error.
static void compute_color_error_for_every_integer_count_and_quantization_level(int encode_hdr_rgb,	// 1 = perform HDR encoding, 0 = perform LDR encoding.
																			   int encode_hdr_alpha, int partition_index, const partition_info * pi,
																				const encoding_choice_errors * eci,	// pointer to the structure for the CURRENT partition.
																			   const endpoints * ep, float4 error_weightings[4],
																			   // arrays to return results back through.
																			   float best_error[21][4], int format_of_choice[21][4])
{
	int i;
	int partition_size = pi->texels_per_partition[partition_index];

	static const float baseline_quant_error[21] = {
		(65536.0f * 65536.0f / 18.0f),				// 2 values, 1 step
		(65536.0f * 65536.0f / 18.0f) / (2 * 2),	// 3 values, 2 steps
		(65536.0f * 65536.0f / 18.0f) / (3 * 3),	// 4 values, 3 steps
		(65536.0f * 65536.0f / 18.0f) / (4 * 4),	// 5 values
		(65536.0f * 65536.0f / 18.0f) / (5 * 5),
		(65536.0f * 65536.0f / 18.0f) / (7 * 7),
		(65536.0f * 65536.0f / 18.0f) / (9 * 9),
		(65536.0f * 65536.0f / 18.0f) / (11 * 11),
		(65536.0f * 65536.0f / 18.0f) / (15 * 15),
		(65536.0f * 65536.0f / 18.0f) / (19 * 19),
		(65536.0f * 65536.0f / 18.0f) / (23 * 23),
		(65536.0f * 65536.0f / 18.0f) / (31 * 31),
		(65536.0f * 65536.0f / 18.0f) / (39 * 39),
		(65536.0f * 65536.0f / 18.0f) / (47 * 47),
		(65536.0f * 65536.0f / 18.0f) / (63 * 63),
		(65536.0f * 65536.0f / 18.0f) / (79 * 79),
		(65536.0f * 65536.0f / 18.0f) / (95 * 95),
		(65536.0f * 65536.0f / 18.0f) / (127 * 127),
		(65536.0f * 65536.0f / 18.0f) / (159 * 159),
		(65536.0f * 65536.0f / 18.0f) / (191 * 191),
		(65536.0f * 65536.0f / 18.0f) / (255 * 255)
	};

	float4 ep0 = ep->endpt0[partition_index];
	float4 ep1 = ep->endpt1[partition_index];

	float ep0_max = MAX(MAX(ep0.x, ep0.y), ep0.z);
	float ep0_min = MIN(MIN(ep0.x, ep0.y), ep0.z);
	float ep1_max = MAX(MAX(ep1.x, ep1.y), ep1.z);
	float ep1_min = MIN(MIN(ep1.x, ep1.y), ep1.z);

	ep0_min = MAX(ep0_min, 0.0f);
	ep1_min = MAX(ep1_min, 0.0f);
	ep0_max = MAX(ep0_max, 1e-10f);
	ep1_max = MAX(ep1_max, 1e-10f);

	float4 error_weight = error_weightings[partition_index];

	float error_weight_rgbsum = error_weight.x + error_weight.y + error_weight.z;

	float range_upper_limit_rgb = encode_hdr_rgb ? 61440.0f : 65535.0f;
	float range_upper_limit_alpha = encode_hdr_alpha ? 61440.0f : 65535.0f;

	// it is possible to get endpoint colors significantly outside [0,upper-limit]
	// even if the input data are safely contained in [0,upper-limit];
	// we need to add an error term for this situation,
	float4 ep0_range_error_high;
	float4 ep1_range_error_high;
	float4 ep0_range_error_low;
	float4 ep1_range_error_low;

	ep0_range_error_high.x = MAX(0.0f, ep0.x - range_upper_limit_rgb);
	ep0_range_error_high.y = MAX(0.0f, ep0.y - range_upper_limit_rgb);
	ep0_range_error_high.z = MAX(0.0f, ep0.z - range_upper_limit_rgb);
	ep0_range_error_high.w = MAX(0.0f, ep0.w - range_upper_limit_alpha);
	ep1_range_error_high.x = MAX(0.0f, ep1.x - range_upper_limit_rgb);
	ep1_range_error_high.y = MAX(0.0f, ep1.y - range_upper_limit_rgb);
	ep1_range_error_high.z = MAX(0.0f, ep1.z - range_upper_limit_rgb);
	ep1_range_error_high.w = MAX(0.0f, ep1.w - range_upper_limit_alpha);

	ep0_range_error_low.x = MIN(0.0f, ep0.x);
	ep0_range_error_low.y = MIN(0.0f, ep0.y);
	ep0_range_error_low.z = MIN(0.0f, ep0.z);
	ep0_range_error_low.w = MIN(0.0f, ep0.w);
	ep1_range_error_low.x = MIN(0.0f, ep1.x);
	ep1_range_error_low.y = MIN(0.0f, ep1.y);
	ep1_range_error_low.z = MIN(0.0f, ep1.z);
	ep1_range_error_low.w = MIN(0.0f, ep1.w);

	float4 sum_range_error =
		(ep0_range_error_low * ep0_range_error_low) + (ep1_range_error_low * ep1_range_error_low) + (ep0_range_error_high * ep0_range_error_high) + (ep1_range_error_high * ep1_range_error_high);
	float rgb_range_error = dot(sum_range_error.xyz, error_weight.xyz) * 0.5f * partition_size;
	float alpha_range_error = sum_range_error.w * error_weight.w * 0.5f * partition_size;


	#ifdef DEBUG_PRINT_DIAGNOSTICS
		if (print_diagnostics)
		{
			printf("%s : partition=%d\nrgb-error_wt=%f  alpha_error_wt=%f\n", __func__, partition_index, error_weight_rgbsum, error_weight.w);

			printf("ep0 = %f %f %f %f\n", ep0.x, ep0.y, ep0.z, ep0.w);
			printf("ep1 = %f %f %f %f\n", ep1.x, ep1.y, ep1.z, ep1.w);


			printf("rgb_range_error = %f, alpha_range_error = %f\n", rgb_range_error, alpha_range_error);

			printf("rgb-luma-error: %f\n", eci->rgb_luma_error);
		}
	#endif

	if (encode_hdr_rgb)
	{

		// collect some statistics
		float af, cf;
		if (ep1.x > ep1.y && ep1.x > ep1.z)
		{
			af = ep1.x;
			cf = ep1.x - ep0.x;
		}
		else if (ep1.y > ep1.z)
		{
			af = ep1.y;
			cf = ep1.y - ep0.y;
		}
		else
		{
			af = ep1.z;
			cf = ep1.z - ep0.z;
		}

		float bf = af - ep1_min;	// estimate of color-component spread in high endpoint color
		float3 prd = ep1.xyz - float3(cf, cf, cf);
		float3 pdif = prd - ep0.xyz;
		// estimate of color-component spread in low endpoint color
		float df = MAX(MAX(fabs(pdif.x), fabs(pdif.y)), fabs(pdif.z));

		int b = (int)bf;
		int c = (int)cf;
		int d = (int)df;

		// determine which one of the 6 submodes is likely to be used in
		// case of an RGBO-mode
		int rgbo_mode = 5;		// 7 bits per component
		// mode 4: 8 7 6
		if (b < 32768 && c < 16384)
			rgbo_mode = 4;
		// mode 3: 9 6 7
		if (b < 8192 && c < 16384)
			rgbo_mode = 3;
		// mode 2: 10 5 8
		if (b < 2048 && c < 16384)
			rgbo_mode = 2;
		// mode 1: 11 6 5
		if (b < 2048 && c < 1024)
			rgbo_mode = 1;
		// mode 0: 11 5 7
		if (b < 1024 && c < 4096)
			rgbo_mode = 0;

		// determine which one of the 9 submodes is likely to be used in
		// case of an RGB-mode.
		int rgb_mode = 8;		// 8 bits per component, except 7 bits for blue

		// mode 0: 9 7 6 7
		if (b < 16384 && c < 8192 && d < 8192)
			rgb_mode = 0;
		// mode 1: 9 8 6 6
		if (b < 32768 && c < 8192 && d < 4096)
			rgb_mode = 1;
		// mode 2: 10 6 7 7
		if (b < 4096 && c < 8192 && d < 4096)
			rgb_mode = 2;
		// mode 3: 10 7 7 6
		if (b < 8192 && c < 8192 && d < 2048)
			rgb_mode = 3;
		// mode 4: 11 8 6 5
		if (b < 8192 && c < 2048 && d < 512)
			rgb_mode = 4;
		// mode 5: 11 6 8 6
		if (b < 2048 && c < 8192 && d < 1024)
			rgb_mode = 5;
		// mode 6: 12 7 7 5
		if (b < 2048 && c < 2048 && d < 256)
			rgb_mode = 6;
		// mode 7: 12 6 7 6
		if (b < 1024 && c < 2048 && d < 512)
			rgb_mode = 7;

		static const float rgbo_error_scales[6] = { 4.0f, 4.0f, 16.0f, 64.0f, 256.0f, 1024.0f };
		static const float rgb_error_scales[9] = { 64.0f, 64.0f, 16.0f, 16.0f, 4.0f, 4.0f, 1.0f, 1.0f, 384.0f };

		float mode7mult = rgbo_error_scales[rgbo_mode] * 0.0015f;	// empirically determined ....
		float mode11mult = rgb_error_scales[rgb_mode] * 0.010f;	// empirically determined ....


		float lum_high = (ep1.x + ep1.y + ep1.z) * (1.0f / 3.0f);
		float lum_low = (ep0.x + ep0.y + ep0.z) * (1.0f / 3.0f);
		float lumdif = lum_high - lum_low;
		float mode23mult = lumdif < 960 ? 4.0f : lumdif < 3968 ? 16.0f : 128.0f;

		mode23mult *= 0.0005f;	// empirically determined ....

		// pick among the available HDR endpoint modes
		for (i = 0; i < 8; i++)
		{
			best_error[i][3] = 1e30f;
			format_of_choice[i][3] = encode_hdr_alpha ? FMT_HDR_RGBA : FMT_HDR_RGB_LDR_ALPHA;
			best_error[i][2] = 1e30f;
			format_of_choice[i][2] = FMT_HDR_RGB;
			best_error[i][1] = 1e30f;
			format_of_choice[i][1] = FMT_HDR_RGB_SCALE;
			best_error[i][0] = 1e30f;
			format_of_choice[i][0] = FMT_HDR_LUMINANCE_LARGE_RANGE;
		}

		for (i = 8; i < 21; i++)
		{
			// base_quant_error should depend on the scale-factor that would be used
			// during actual encode of the color value.

			float base_quant_error = baseline_quant_error[i] * partition_size * 1.0f;
			float rgb_quantization_error = error_weight_rgbsum * base_quant_error * 2.0f;
			float alpha_quantization_error = error_weight.w * base_quant_error * 2.0f;
			float rgba_quantization_error = rgb_quantization_error + alpha_quantization_error;

			#ifdef DEBUG_PRINT_DIAGNOSTICS
				if (print_diagnostics)
					printf("rgba-quant = %f can_offset_encode=%d\n", rgba_quantization_error, eci->can_offset_encode);
			#endif

			// for 8 integers, we have two encodings: one with HDR alpha and another one
			// with LDR alpha.

			float full_hdr_rgba_error = rgba_quantization_error + rgb_range_error + alpha_range_error;
			best_error[i][3] = full_hdr_rgba_error;
			format_of_choice[i][3] = encode_hdr_alpha ? FMT_HDR_RGBA : FMT_HDR_RGB_LDR_ALPHA;

			// for 6 integers, we have one HDR-RGB encoding
			float full_hdr_rgb_error = (rgb_quantization_error * mode11mult) + rgb_range_error + eci->alpha_drop_error;
			best_error[i][2] = full_hdr_rgb_error;
			format_of_choice[i][2] = FMT_HDR_RGB;

			// for 4 integers, we have one HDR-RGB-Scale encoding
			float hdr_rgb_scale_error = (rgb_quantization_error * mode7mult) + rgb_range_error + eci->alpha_drop_error + eci->rgb_luma_error;

			best_error[i][1] = hdr_rgb_scale_error;
			format_of_choice[i][1] = FMT_HDR_RGB_SCALE;

			// for 2 integers, we assume luminance-with-large-range
			float hdr_luminance_error = (rgb_quantization_error * mode23mult) + rgb_range_error + eci->alpha_drop_error + eci->luminance_error;
			best_error[i][0] = hdr_luminance_error;
			format_of_choice[i][0] = FMT_HDR_LUMINANCE_LARGE_RANGE;

			#ifdef DEBUG_PRINT_DIAGNOSTICS
				if (print_diagnostics)
				{
					for (int j = 0; j < 4; j++)
					{
						printf("(hdr) quant-level=%d ints=%d format=%d error=%f\n", i, j, format_of_choice[i][j], best_error[i][j]);
					}
				}
			#endif
		}
	}
	else
	{
		for (i = 0; i < 4; i++)
		{
			best_error[i][3] = 1e30f;
			best_error[i][2] = 1e30f;
			best_error[i][1] = 1e30f;
			best_error[i][0] = 1e30f;

			format_of_choice[i][3] = FMT_RGBA;
			format_of_choice[i][2] = FMT_RGB;
			format_of_choice[i][1] = FMT_RGB_SCALE;
			format_of_choice[i][0] = FMT_LUMINANCE;
		}

		// pick among the available LDR endpoint modes
		for (i = 4; i < 21; i++)
		{
			float base_quant_error = baseline_quant_error[i] * partition_size * 1.0f;
			float rgb_quantization_error = error_weight_rgbsum * base_quant_error;
			float alpha_quantization_error = error_weight.w * base_quant_error;
			float rgba_quantization_error = rgb_quantization_error + alpha_quantization_error;

			#ifdef DEBUG_PRINT_DIAGNOSTICS
				if (print_diagnostics)
					printf("rgba-quant = %f can_offset_encode=%d\n", rgba_quantization_error, eci->can_offset_encode);
			#endif

			// for 8 integers, the available encodings are:
			// full LDR RGB-Alpha
			float full_ldr_rgba_error = rgba_quantization_error;
			if (eci->can_blue_contract)
				full_ldr_rgba_error *= 0.625f;
			if (eci->can_offset_encode && i <= 18)
				full_ldr_rgba_error *= 0.5f;
			full_ldr_rgba_error += rgb_range_error + alpha_range_error;

			best_error[i][3] = full_ldr_rgba_error;
			format_of_choice[i][3] = FMT_RGBA;

			// for 6 integers, we have:
			// - an LDR-RGB encoding
			// - an RGBS + Alpha encoding (LDR)

			float full_ldr_rgb_error = rgb_quantization_error;
			if (eci->can_blue_contract)
				full_ldr_rgb_error *= 0.5f;
			if (eci->can_offset_encode && i <= 18)
				full_ldr_rgb_error *= 0.25f;
			full_ldr_rgb_error += eci->alpha_drop_error + rgb_range_error;

			float rgbs_alpha_error = rgba_quantization_error + eci->rgb_scale_error + rgb_range_error + alpha_range_error;

			if (rgbs_alpha_error < full_ldr_rgb_error)
			{
				best_error[i][2] = rgbs_alpha_error;
				format_of_choice[i][2] = FMT_RGB_SCALE_ALPHA;
			}
			else
			{
				best_error[i][2] = full_ldr_rgb_error;
				format_of_choice[i][2] = FMT_RGB;
			}

			// for 4 integers, we have a Luminance-Alpha encoding and the RGBS encoding
			float ldr_rgbs_error = rgb_quantization_error + eci->alpha_drop_error + eci->rgb_scale_error + rgb_range_error;

			float lum_alpha_error = rgba_quantization_error + eci->luminance_error + rgb_range_error + alpha_range_error;

			if (ldr_rgbs_error < lum_alpha_error)
			{
				best_error[i][1] = ldr_rgbs_error;
				format_of_choice[i][1] = FMT_RGB_SCALE;
			}
			else
			{
				best_error[i][1] = lum_alpha_error;
				format_of_choice[i][1] = FMT_LUMINANCE_ALPHA;
			}

			// for 2 integers, we have a Luminance-encoding and an Alpha-encoding.
			float luminance_error = rgb_quantization_error + eci->alpha_drop_error + eci->luminance_error + rgb_range_error;

			best_error[i][0] = luminance_error;
			format_of_choice[i][0] = FMT_LUMINANCE;

			#ifdef DEBUG_PRINT_DIAGNOSTICS
				if (print_diagnostics)
				{
					for (int j = 0; j < 4; j++)
					{
						printf(" (ldr) quant-level=%d ints=%d format=%d error=%f\n", i, j, format_of_choice[i][j], best_error[i][j]);
					}
				}
			#endif
		}
	}
}

// for 1 partition, find the best combination (one format + a quantization level) for a given bitcount
static void one_partition_find_best_combination_for_bitcount(float combined_best_error[21][4],
															 int formats_of_choice[21][4], int bits_available, int *best_quantization_level, int *best_formats, float *error_of_best_combination)
{
	int i;
	int best_integer_count = -1;
	float best_integer_count_error = 1e20f;
	for (i = 0; i < 4; i++)
	{
		// compute the quantization level for a given number of integers and a given number of bits.
		int quantization_level = quantization_mode_table[i + 1][bits_available];
		if (quantization_level == -1)
			continue;			// used to indicate the case where we don't have enough bits to represent a given endpoint format at all.
		if (combined_best_error[quantization_level][i] < best_integer_count_error)
		{
			best_integer_count_error = combined_best_error[quantization_level][i];
			best_integer_count = i;
		}
	}

	int ql = quantization_mode_table[best_integer_count + 1][bits_available];

	*best_quantization_level = ql;
	*error_of_best_combination = best_integer_count_error;
	if (ql >= 0)
		*best_formats = formats_of_choice[ql][best_integer_count];
	else
		*best_formats = FMT_LUMINANCE;
}

// for 2 partitions, find the best format combinations for every (quantization-mode, integer-count) combination
static void two_partitions_find_best_combination_for_every_quantization_and_integer_count(float best_error[2][21][4],	// indexed by (partition, quant-level, integer-pair-count-minus-1)
																						  int format_of_choice[2][21][4],
																						  float combined_best_error[21][7],	// indexed by (quant-level, integer-pair-count-minus-2)
																						  int formats_of_choice[21][7][2])
{
	int i, j;

	for (i = 0; i < 21; i++)
		for (j = 0; j < 7; j++)
			combined_best_error[i][j] = 1e30f;

	int quant;
	for (quant = 5; quant < 21; quant++)
	{
		for (i = 0; i < 4; i++)	// integer-count for first endpoint-pair
		{
			for (j = 0; j < 4; j++)	// integer-count for second endpoint-pair
			{
				int low2 = MIN(i, j);
				int high2 = MAX(i, j);
				if ((high2 - low2) > 1)
					continue;

				int intcnt = i + j;
				float errorterm = MIN(best_error[0][quant][i] + best_error[1][quant][j], 1e10f);
				if (errorterm <= combined_best_error[quant][intcnt])
				{
					combined_best_error[quant][intcnt] = errorterm;
					formats_of_choice[quant][intcnt][0] = format_of_choice[0][quant][i];
					formats_of_choice[quant][intcnt][1] = format_of_choice[1][quant][j];
				}
			}
		}
	}
}

// for 2 partitions, find the best combination (two formats + a quantization level) for a given bitcount
static void two_partitions_find_best_combination_for_bitcount(float combined_best_error[21][7],
															  int formats_of_choice[21][7][2],
															  int bits_available, int *best_quantization_level, int *best_quantization_level_mod, int *best_formats, float *error_of_best_combination)
{
	int i;

	int best_integer_count = 0;
	float best_integer_count_error = 1e20f;
	int integer_count;

	for (integer_count = 2; integer_count <= 8; integer_count++)
	{
		// compute the quantization level for a given number of integers and a given number of bits.
		int quantization_level = quantization_mode_table[integer_count][bits_available];
		if (quantization_level == -1)
			break;				// used to indicate the case where we don't have enough bits to represent a given endpoint format at all.
		float integer_count_error = combined_best_error[quantization_level][integer_count - 2];
		if (integer_count_error < best_integer_count_error)
		{
			best_integer_count_error = integer_count_error;
			best_integer_count = integer_count;
		}
	}

	int ql = quantization_mode_table[best_integer_count][bits_available];
	int ql_mod = quantization_mode_table[best_integer_count][bits_available + 2];

	*best_quantization_level = ql;
	*best_quantization_level_mod = ql_mod;
	*error_of_best_combination = best_integer_count_error;
	if (ql >= 0)
	{
		for (i = 0; i < 2; i++)
			best_formats[i] = formats_of_choice[ql][best_integer_count - 2][i];
	}
	else
	{
		for (i = 0; i < 2; i++)
			best_formats[i] = FMT_LUMINANCE;
	}
}

// for 3 partitions, find the best format combinations for every (quantization-mode, integer-count) combination
static void three_partitions_find_best_combination_for_every_quantization_and_integer_count(float best_error[3][21][4],	// indexed by (partition, quant-level, integer-count)
																							int format_of_choice[3][21][4], float combined_best_error[21][10], int formats_of_choice[21][10][3])
{
	int i, j, k;

	for (i = 0; i < 21; i++)
		for (j = 0; j < 10; j++)
			combined_best_error[i][j] = 1e30f;

	int quant;
	for (quant = 5; quant < 21; quant++)
	{
		for (i = 0; i < 4; i++)	// integer-count for first endpoint-pair
		{
			for (j = 0; j < 4; j++)	// integer-count for second endpoint-pair
			{
				int low2 = MIN(i, j);
				int high2 = MAX(i, j);
				if ((high2 - low2) > 1)
					continue;
				for (k = 0; k < 4; k++)	// integer-count for third endpoint-pair
				{
					int low3 = MIN(k, low2);
					int high3 = MAX(k, high2);
					if ((high3 - low3) > 1)
						continue;

					int intcnt = i + j + k;
					float errorterm = MIN(best_error[0][quant][i] + best_error[1][quant][j] + best_error[2][quant][k], 1e10f);
					if (errorterm <= combined_best_error[quant][intcnt])
					{
						combined_best_error[quant][intcnt] = errorterm;
						formats_of_choice[quant][intcnt][0] = format_of_choice[0][quant][i];
						formats_of_choice[quant][intcnt][1] = format_of_choice[1][quant][j];
						formats_of_choice[quant][intcnt][2] = format_of_choice[2][quant][k];
					}
				}
			}
		}
	}
}

// for 3 partitions, find the best combination (three formats + a quantization level) for a given bitcount
static void three_partitions_find_best_combination_for_bitcount(float combined_best_error[21][10],
																int formats_of_choice[21][10][3],
																int bits_available, int *best_quantization_level, int *best_quantization_level_mod, int *best_formats, float *error_of_best_combination)
{
	int i;

	int best_integer_count = 0;
	float best_integer_count_error = 1e20f;
	int integer_count;

	for (integer_count = 3; integer_count <= 9; integer_count++)
	{
		// compute the quantization level for a given number of integers and a given number of bits.
		int quantization_level = quantization_mode_table[integer_count][bits_available];
		if (quantization_level == -1)
			break;				// used to indicate the case where we don't have enough bits to represent a given endpoint format at all.
		float integer_count_error = combined_best_error[quantization_level][integer_count - 3];
		if (integer_count_error < best_integer_count_error)
		{
			best_integer_count_error = integer_count_error;
			best_integer_count = integer_count;
		}
	}

	int ql = quantization_mode_table[best_integer_count][bits_available];
	int ql_mod = quantization_mode_table[best_integer_count][bits_available + 5];

	*best_quantization_level = ql;
	*best_quantization_level_mod = ql_mod;
	*error_of_best_combination = best_integer_count_error;
	if (ql >= 0)
	{
		for (i = 0; i < 3; i++)
			best_formats[i] = formats_of_choice[ql][best_integer_count - 3][i];
	}
	else
	{
		for (i = 0; i < 3; i++)
			best_formats[i] = FMT_LUMINANCE;
	}
}

// for 4 partitions, find the best format combinations for every (quantization-mode, integer-count) combination
static void four_partitions_find_best_combination_for_every_quantization_and_integer_count(float best_error[4][21][4],	// indexed by (partition, quant-level, integer-count)
																						   int format_of_choice[4][21][4], float combined_best_error[21][13], int formats_of_choice[21][13][4])
{
	int i, j, k, l;

	for (i = 0; i < 21; i++)
		for (j = 0; j < 13; j++)
			combined_best_error[i][j] = 1e30f;

	int quant;
	for (quant = 5; quant < 21; quant++)
	{
		for (i = 0; i < 4; i++)	// integer-count for first endpoint-pair
		{
			for (j = 0; j < 4; j++)	// integer-count for second endpoint-pair
			{
				int low2 = MIN(i, j);
				int high2 = MAX(i, j);
				if ((high2 - low2) > 1)
					continue;
				for (k = 0; k < 4; k++)	// integer-count for third endpoint-pair
				{
					int low3 = MIN(k, low2);
					int high3 = MAX(k, high2);
					if ((high3 - low3) > 1)
						continue;
					for (l = 0; l < 4; l++)	// integer-count for fourth endpoint-pair
					{
						int low4 = MIN(l, low3);
						int high4 = MAX(l, high3);
						if ((high4 - low4) > 1)
							continue;

						int intcnt = i + j + k + l;
						float errorterm = MIN(best_error[0][quant][i] + best_error[1][quant][j] + best_error[2][quant][k] + best_error[3][quant][l], 1e10f);
						if (errorterm <= combined_best_error[quant][intcnt])
						{
							combined_best_error[quant][intcnt] = errorterm;
							formats_of_choice[quant][intcnt][0] = format_of_choice[0][quant][i];
							formats_of_choice[quant][intcnt][1] = format_of_choice[1][quant][j];
							formats_of_choice[quant][intcnt][2] = format_of_choice[2][quant][k];
							formats_of_choice[quant][intcnt][3] = format_of_choice[3][quant][l];
						}
					}
				}
			}
		}
	}
}

// for 4 partitions, find the best combination (four formats + a quantization level) for a given bitcount
static void four_partitions_find_best_combination_for_bitcount(float combined_best_error[21][13],
															   int formats_of_choice[21][13][4],
															   int bits_available, int *best_quantization_level, int *best_quantization_level_mod, int *best_formats, float *error_of_best_combination)
{
	int i;
	int best_integer_count = 0;
	float best_integer_count_error = 1e20f;
	int integer_count;

	for (integer_count = 4; integer_count <= 9; integer_count++)
	{
		// compute the quantization level for a given number of integers and a given number of bits.
		int quantization_level = quantization_mode_table[integer_count][bits_available];
		if (quantization_level == -1)
			break;				// used to indicate the case where we don't have enough bits to represent a given endpoint format at all.
		float integer_count_error = combined_best_error[quantization_level][integer_count - 4];
		if (integer_count_error < best_integer_count_error)
		{
			best_integer_count_error = integer_count_error;
			best_integer_count = integer_count;
		}
	}

	int ql = quantization_mode_table[best_integer_count][bits_available];
	int ql_mod = quantization_mode_table[best_integer_count][bits_available + 8];

	*best_quantization_level = ql;
	*best_quantization_level_mod = ql_mod;
	*error_of_best_combination = best_integer_count_error;
	if (ql >= 0)
	{
		for (i = 0; i < 4; i++)
			best_formats[i] = formats_of_choice[ql][best_integer_count - 4][i];
	}
	else
	{
		for (i = 0; i < 4; i++)
			best_formats[i] = FMT_LUMINANCE;
	}
}

/*
	The determine_optimal_set_of_endpoint_formats_to_use() function.

	It identifies, for each mode, which set of color endpoint encodings
	produces the best overall result. It then reports back which 4 modes
	look best, along with the ideal color encoding combination for each.

	It takes as input:
		a partitioning an imageblock,
		a set of color endpoints.
		for each mode, the number of bits available for color encoding and the error incurred by quantization.
		in case of 2 plane of weights, a specifier for which color component to use for the second plane of weights.

	It delivers as output for each of the 4 selected modes:
		format specifier
		for each partition
			quantization level to use
			modified quantization level to use
		(when all format specifiers are equal)
*/
void determine_optimal_set_of_endpoint_formats_to_use(int xdim, int ydim, int zdim,
													  const partition_info * pt, const imageblock * blk, const error_weight_block * ewb,
													  const endpoints * ep,
													  int separate_component,	// separate color component for 2-plane mode; -1 for single-plane mode
													  // bitcounts and errors computed for the various quantization methods
													  const int *qwt_bitcounts, const float *qwt_errors,
													  // output data
													  int partition_format_specifiers[4][4], int quantized_weight[4],
													  int quantization_level[4], int quantization_level_mod[4])
{
	int i, j;
	int partition_count = pt->partition_count;

	int encode_hdr_rgb = blk->rgb_lns[0];
	int encode_hdr_alpha = blk->alpha_lns[0];

	// call a helper function to compute the errors that result from various
	// encoding choices (such as using luminance instead of RGB, discarding Alpha,
	// using RGB-scale in place of two separate RGB endpoints and so on)
	encoding_choice_errors eci[4];
	compute_encoding_choice_errors(xdim, ydim, zdim, blk, pt, ewb, separate_component, eci);

	// for each partition, compute the error weights to apply for that partition.
	float4 error_weightings[4];
	float4 dummied_color_scalefactors[4];	// only used to receive data
	compute_partition_error_color_weightings(xdim, ydim, zdim, ewb, pt, error_weightings, dummied_color_scalefactors);

	float best_error[4][21][4];
	int format_of_choice[4][21][4];
	for (i = 0; i < partition_count; i++)
		compute_color_error_for_every_integer_count_and_quantization_level(encode_hdr_rgb, encode_hdr_alpha, i, pt, &(eci[i]), ep, error_weightings, best_error[i], format_of_choice[i]);

	float errors_of_best_combination[MAX_WEIGHT_MODES];
	int best_quantization_levels[MAX_WEIGHT_MODES];
	int best_quantization_levels_mod[MAX_WEIGHT_MODES];
	int best_ep_formats[MAX_WEIGHT_MODES][4];

	// code for the case where the block contains 1 partition
	if (partition_count == 1)
	{
		int best_quantization_level;
		int best_format;
		float error_of_best_combination;
		for (i = 0; i < MAX_WEIGHT_MODES; i++)
		{
			if (qwt_errors[i] >= 1e29f)
			{
				errors_of_best_combination[i] = 1e30f;
				continue;
			}

			one_partition_find_best_combination_for_bitcount(best_error[0], format_of_choice[0], qwt_bitcounts[i], &best_quantization_level, &best_format, &error_of_best_combination);
			error_of_best_combination += qwt_errors[i];

			errors_of_best_combination[i] = error_of_best_combination;
			best_quantization_levels[i] = best_quantization_level;
			best_quantization_levels_mod[i] = best_quantization_level;
			best_ep_formats[i][0] = best_format;
		}
	}
	// code for the case where the block contains 2 partitions
	else if (partition_count == 2)
	{
		int best_quantization_level;
		int best_quantization_level_mod;
		int best_formats[2];
		float error_of_best_combination;

		float combined_best_error[21][7];
		int formats_of_choice[21][7][2];

		two_partitions_find_best_combination_for_every_quantization_and_integer_count(best_error, format_of_choice, combined_best_error, formats_of_choice);


		for (i = 0; i < MAX_WEIGHT_MODES; i++)
		{
			if (qwt_errors[i] >= 1e29f)
			{
				errors_of_best_combination[i] = 1e30f;
				continue;
			}

			two_partitions_find_best_combination_for_bitcount(combined_best_error, formats_of_choice, qwt_bitcounts[i],
															  &best_quantization_level, &best_quantization_level_mod, best_formats, &error_of_best_combination);

			error_of_best_combination += qwt_errors[i];

			errors_of_best_combination[i] = error_of_best_combination;
			best_quantization_levels[i] = best_quantization_level;
			best_quantization_levels_mod[i] = best_quantization_level_mod;
			best_ep_formats[i][0] = best_formats[0];
			best_ep_formats[i][1] = best_formats[1];
		}
	}
	// code for the case where the block contains 3 partitions
	else if (partition_count == 3)
	{
		int best_quantization_level;
		int best_quantization_level_mod;
		int best_formats[3];
		float error_of_best_combination;

		float combined_best_error[21][10];
		int formats_of_choice[21][10][3];

		three_partitions_find_best_combination_for_every_quantization_and_integer_count(best_error, format_of_choice, combined_best_error, formats_of_choice);

		for (i = 0; i < MAX_WEIGHT_MODES; i++)
		{
			if (qwt_errors[i] >= 1e29f)
			{
				errors_of_best_combination[i] = 1e30f;
				continue;
			}

			three_partitions_find_best_combination_for_bitcount(combined_best_error,
																formats_of_choice, qwt_bitcounts[i], &best_quantization_level, &best_quantization_level_mod, best_formats, &error_of_best_combination);
			error_of_best_combination += qwt_errors[i];

			errors_of_best_combination[i] = error_of_best_combination;
			best_quantization_levels[i] = best_quantization_level;
			best_quantization_levels_mod[i] = best_quantization_level_mod;
			best_ep_formats[i][0] = best_formats[0];
			best_ep_formats[i][1] = best_formats[1];
			best_ep_formats[i][2] = best_formats[2];
		}
	}
	// code for the case where the block contains 4 partitions
	else if (partition_count == 4)
	{
		int best_quantization_level;
		int best_quantization_level_mod;
		int best_formats[4];
		float error_of_best_combination;

		float combined_best_error[21][13];
		int formats_of_choice[21][13][4];

		four_partitions_find_best_combination_for_every_quantization_and_integer_count(best_error, format_of_choice, combined_best_error, formats_of_choice);

		for (i = 0; i < MAX_WEIGHT_MODES; i++)
		{
			if (qwt_errors[i] >= 1e29f)
			{
				errors_of_best_combination[i] = 1e30f;
				continue;
			}
			four_partitions_find_best_combination_for_bitcount(combined_best_error,
															   formats_of_choice, qwt_bitcounts[i], &best_quantization_level, &best_quantization_level_mod, best_formats, &error_of_best_combination);
			error_of_best_combination += qwt_errors[i];

			errors_of_best_combination[i] = error_of_best_combination;
			best_quantization_levels[i] = best_quantization_level;
			best_quantization_levels_mod[i] = best_quantization_level_mod;
			best_ep_formats[i][0] = best_formats[0];
			best_ep_formats[i][1] = best_formats[1];
			best_ep_formats[i][2] = best_formats[2];
			best_ep_formats[i][3] = best_formats[3];
		}
	}

	// finally, go through the results and pick the 4 best-looking modes.
	int best_error_weights[4];

	for (i = 0; i < 4; i++)
	{
		float best_ep_error = 1e30f;
		int best_error_index = -1;
		for (j = 0; j < MAX_WEIGHT_MODES; j++)
		{
			if (errors_of_best_combination[j] < best_ep_error && best_quantization_levels[j] >= 5)
			{
				best_ep_error = errors_of_best_combination[j];
				best_error_index = j;
			}
		}
		best_error_weights[i] = best_error_index;

		if(best_error_index >= 0)
		{
			errors_of_best_combination[best_error_index] = 1e30f;
		}
	}

	for (i = 0; i < 4; i++)
	{
		quantized_weight[i] = best_error_weights[i];
		if (quantized_weight[i] >= 0)
		{
			quantization_level[i] = best_quantization_levels[best_error_weights[i]];
			quantization_level_mod[i] = best_quantization_levels_mod[best_error_weights[i]];
			for (j = 0; j < partition_count; j++)
			{
				partition_format_specifiers[i][j] = best_ep_formats[best_error_weights[i]][j];
			}
		}
	}
}